Rigid Flat Punch on Flat: Online Calculator

18.05.2021

indentation by a rigid flat punch

Indentation by a Rigid Flat Punch

This calculator allows calculating pressure $p$ , displacement (elastic deformation) $w$ , stiffness $k_z$ , average pressure $p_0$ and resultant force $F_N$ for the case of indentation of an elastic half-space by a rigid cylindrical flat indenter. In this case, the intender is rigid and of cylindrical shape. The substrate is elastic, the geometric parameters $d$ – rigid body displacement, $a$ – radius of the cylinder and material parameters $E^*=E/(1-\nu^2)$ are the inputs (see the figure and definitions below). The stress distribution in the contact area and the displacements of the half-space outside the contact are:

(1) $\begin{align*} \sigma_{zz}(r;d) &= - \frac{E^*d}{\pi \sqrt{a^2 - r^2}}, \hspace{1cm}r \leq a \\ w(r;d) &= \frac{2d}{\pi} \arcsin(\frac{a}{r}), \hspace{1cm} r > a \end{align*}$

where $d$ is the maximum displacement due to the deformation, $a$ is the radius of the punch and $r$ is the radial coordinate.

The contact stiffness can be calculated as follows:

(2) $\begin{align*} k_z &= 2E^*a, \hspace{1cm}\\ \end{align*}$

Equations were taken from [1].

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Definitions:

Poisson’s ratio $\nu$ dimensionless,
Young’s modulus of elasticity $E$ , [Pa],
Equivalent elastic constant $E^* = \left( \frac{1-\nu^2}{E} \right)^{-1}$ , [Pa],
Normal load $F$ , [N]

Take a look at other calculators: https://www.tribonet.org/calculators/.

References:

[1] Valentin L. Popov, Hanbook of Contact Mechnics, Exact Solutions of Axisymmetric Contact Problems, pg. 11

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